This paper reviews the architecture of amylose supramolecules in form of inclusion complexes with synthetic polymers by phosphorylase-catalyzed enzymatic polymerization. Amylose is known to be synthesized by enzymatic polymerization using α-d-glucose 1-phosphate as a monomer, by phosphorylase catalysis. When the phosphorylase-catalyzed enzymatic polymerization was conducted in the presence of various hydrophobic polymers, such as polyethers, polyesters, poly(ester-ether), and polycarbonates as a guest polymer, such inclusion supramolecules were formed by the hydrophobic interaction in the progress of polymerization. Because the representation of propagation in the polymerization is similar to the way that a vine of a plant grows, twining around a rod, this polymerization method for the formation of amylose-polymer inclusion complexes was proposed to be named "vine-twining polymerization". To yield an inclusion complex from a strongly hydrophobic polyester, the parallel enzymatic polymerization system was extensively developed. The author found that amylose selectively included one side of the guest polymer from a mixture of two resemblant guest polymers, as well as a specific range in molecular weights of the guest polymers poly(tetrahydrofuran) (PTHF) in the vine-twining polymerization. Selective inclusion behavior of amylose toward stereoisomers of chiral polyesters, poly(lactide)s, also appeared in the vine-twining polymerization.